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On the existence of saddle points for nonlinear second-order cone programming problems

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  • Jinchuan Zhou
  • Jein-Shan Chen

Abstract

In this paper, we study the existence of local and global saddle points for nonlinear second-order cone programming problems. The existence of local saddle points is developed by using the second-order sufficient conditions, in which a sigma-term is added to reflect the curvature of second-order cone. Furthermore, by dealing with the perturbation of the primal problem, we establish the existence of global saddle points, which can be applicable for the case of multiple optimal solutions. The close relationship between global saddle points and exact penalty representations are discussed as well. Copyright Springer Science+Business Media New York 2015

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  • Jinchuan Zhou & Jein-Shan Chen, 2015. "On the existence of saddle points for nonlinear second-order cone programming problems," Journal of Global Optimization, Springer, vol. 62(3), pages 459-480, July.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:3:p:459-480
    DOI: 10.1007/s10898-014-0252-5
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    References listed on IDEAS

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    Cited by:

    1. M. V. Dolgopolik, 2018. "Augmented Lagrangian functions for cone constrained optimization: the existence of global saddle points and exact penalty property," Journal of Global Optimization, Springer, vol. 71(2), pages 237-296, June.

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